Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets

By M. Young. 2014

92 citations recorded by the source corpus.

We prove a Weyl-type subconvexity bound for the central value of the $L$-function of a Hecke-Maass form or a holomorphic Hecke eigenform twisted by a quadratic Dirichlet character, uniform in the archimedean parameter as well as the twisting parameter. A similar hybrid bound holds for quadratic Dirichlet $L$-functions, improving on a result of Heath-Brown. As a consequence of these new bounds, we obtain explicit estimates for the number of Heegner points of large odd discriminant in shrinking sets.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/836b3247522f31e33f7a939619ee7cc2d9da5898

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In Applied Mathematics

1. Ian Petrow
2. M. Young
3. A. Shankar
4. Manjul Bhargava
5. Siegfred Baluyot

In Geometry and Topology

1. Ian Petrow
2. M. Young

Citations in the corpus

• A generalized cubic moment and the Petersson formula for newforms (2016, methodology): “nds of [CI] do not apply, and so the methods developed in this paper pave the way for further improvements. A GENERALIZED CUBIC MOMENT AND THE PETERSSON FORMULA FOR NEWFORMS 5 The second-named author [Y1] generalized the [CI] method allowing for large weights (or spectral parameters, in the Maass ca”
• The Weyl bound for Dirichlet L-functions of cube-free conductor (2018, background): “) is the analytic conductor of the automorphic L-function L(1/2,π). The Weyl bound is only known in a few cases, notably for quadratic twists of certain self-dual GL2 automorphic forms; see [CI] [Iv] [Y1] [PY1] for example. Estimating the Dirichlet L-functions L(1/2,χ) of conductor qas q→ ∞ is analo”